CALC Debye’s T 3 ?Law. At very low temperatures the molar heat capacity of rock salt varies with temperature according to Debye’s T3 law: where k = 1940 J/mol ? K and ? = 281 K. (a) How much heat is required to raise the temperature of 1.50 mol of rock salt from 10.0 K to 40.0 K? (?Hint: Use Eq. (17.18) in the form dQ = nCdT and integrate.) (b) What is the average molar heat capacity in this range? (c) What is the true molar heat capacity at 40.0 K?

Solution 95P Step 1 of 6: (a) How much heat is required to raise the temperature of 1.50 mol of rock salt from 10.0 K to 40.0 K (H int: Use Eq. (17.18) in the form dQ = nCdT and integrate.) Given data, Initial temperature,T =i10k Final temperature, T = 40k f Number of moles, n = 1.5 mol k= 1940 J/mol. K Debye temperature, = 281 k Molar specific heat is the energy required to raise the temperature of one mole of substance by one degree. That is given by 3 Molar heat capacity, c = k T3